Method and apparatus for resolving individual signals in detector output data

ABSTRACT

A method and apparatus for resolving individual signals in a radiation detector output data. The method comprising: obtaining a signal form characterizing the detector; obtaining digitized detector output data in a form of a digital time series; making parameter estimates of one or more parameters of at least one signal present in the detector output data, wherein the one or more parameters comprise at least a signal temporal position of the at least one signal; forming a mathematical model based on the digital time series and as a function of at least the signal form, the temporal position of the at least one signal, and an amplitude of the at least one signal; and determining the amplitude of the at least one signal based on the mathematical model, the amplitude being indicative of a radiation event.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/685,719, filed Mar. 13, 2007, titled “METHOD AND APPARATUS FORRESOLVING INDIVIDUAL SIGNALS IN DETECTOR OUTPUT DATA,” which is acontinuation of International Application No. PCT/AU2005/001423, filedSep. 16, 2005, which claims the benefit of Australian Patent ApplicationNo. 2004905364, filed Sep. 16, 2004. Each of the foregoing applicationsis incorporated by reference in its entirety.

BACKGROUND

1. Field

The present invention relates generally to the field of the detectionand measurement of radiation and in particular, though not exclusively,to a method and apparatus for the recovery, from a radiation detector,of data affected by pulse pile-up.

2. Description of the Related Technology

The accurate detection and measurement of radiation is employed in manyindustries including homeland security, scientific instrumentation,medical imaging and the minerals processing industry. These and otherindustries use the detection and measurement of radiation for thenon-invasive analysis of materials or other specimens. Transmissionbased imaging, spectroscopic analysis or other modalities can be used toperform such analysis.

Spectroscopy, for example, is commonly used to analyze materials.Knowledge about the material is obtained by analysis of radiationemission from elements within the specimen. This emission of radiationcan be stimulated emission due to some form of incident radiation or theresult of natural emission from the constituent elements.

Gamma-ray spectroscopy, for example, is a form of spectroscopy in whichthe emitted electromagnetic radiation is in the form of gamma-rays. Ingamma-ray spectroscopy the detection of the resulting radiation iscommonly performed with a scintillation crystal (such asthallium-activated sodium iodide, NaI(Tl)), though there are a number ofother detector types that can also be used. NaI(Tl) crystals generateultra-violet photons pursuant to incident gamma-ray radiation. Thesephotons may then be directed to a photomultiplier tube (PMT) whichgenerates a corresponding electrical signal or pulse. As a result, theinteraction between the photons and the detector gives rise topulse-like signals, the shape of which is determined by the incidentgamma-ray radiation, the detecting crystal and the PMT. The fundamentalform of these pulse-like signals is referred to as the impulse responseof the detector.

The output from the photomultiplier is an electrical signal representingthe summation of input signals, of determined form, generated inresponse to discrete gamma rays arriving at the scintillation crystal.By examining the detector output over time, and in particular theamplitude of the component signals, it is possible to deduce informationregarding the chemical composition of the material.

Analysis by gamma-ray spectroscopy requires the characterization of theindividual signals generated in response to incident gamma-rays. Signalparameters of particular interest include signal amplitude, number andtime of occurrence or temporal position (whether measured as time ofarrival, time of maximum or otherwise). If the arrival times of twogamma-rays differ by more than the response time of the detector,analysis of the detector output is relatively straightforward. However,in many applications a high flux of gamma-rays cannot be avoided, or maybe desirable so that spectroscopic analysis can be performed in areasonable time period. As the time between the arrivals of gamma-raysdecreases, characterization of all resultant signals becomes difficult.

In particular, the analysis is affected by a phenomenon known as pulsepile-up [G. F. Knoll, Radiation Detection and Measurement, 3rd edition,Chapter 17, pp. 632-634, 658 and 659, John Wiley and Sons, New York2000], whereby multiple gamma-rays arriving more or less simultaneouslyproduce signals which sum together and may be counted as a singlesignal. The magnitude of this combined signal is greater than theindividual components, leading to errors in later analysis.

The energy of an incident gamma-ray may be reflected in the amplitude ofthe pulse-like signal produced by the detector. The presence of specificgamma-ray energies within the detector signal is indicative ofparticular elements in the material from which gamma-rays originate.Thus, a failure to differentiate a large amplitude signal caused by asingle scintillation event from the superposition of multiple events canhave a serious effect on the accuracy of subsequent spectroscopicanalysis.

Some existing techniques aim to prevent corruption of the spectroscopicanalysis due to pulse pile-up. Certain pulse shaping electronics havebeen shown to reduce the response time of the detector resulting in adiminished prevalence of pile-up in the final spectrum [A. Pullia, A.Geraci and G. Ripamonti, Quasioptimum γ and X-Ray Spectroscopy Based onReal-Time Digital Techniques, Nucl. Inst. and Meth. A 439 (2000)378-384]. This technique is limited, however, by detector response time.Another approach is ‘pulse pile-up rejection’ whereby signals suspectedto contain pulse pipe-up are discarded. Only signals free from pulsepile-up are used in spectroscopic analysis. However, as the rate ofradiation incident on the detector increases, so too does the likelihoodthat pulse pile-up will occur and the more it is necessary to discarddata. Accordingly, existing pulse pile-up rejection is of limitedusefulness since a state is quickly reached beyond which a higherincident radiation flux ceases to reduce the time needed for analysis,as an increasing percentage of data must be rejected.

A more sophisticated approach is to make use of prior knowledge aboutthe profile of a single pulse from the detector or to modelmathematically the parameters of a signal. It is then possible inprinciple to distinguish signals or pulses that originate from a singleevent from those caused by pulse pile-up. In one such method of analysis[R. J. Komar and H.-B. Mak, Digital signal processing for BGO detectors,Nucl. Inst. and Meth. A 336 (1993) 246-252], signals that depart fromthe simple profile are selected for subsequent analysis. This analysisinvolves fitting, via an iterative process, two pulses of varyingseparation and amplitude. Once the fit has been determined, thecharacteristics of the individual pulses are known from the fittingparameters and hence a pulse arising from two closely occurring signalscan be decomposed into the corresponding discrete signals. However, thisapproach fails to accommodate circumstances where pulse pile-up iscaused by the superposition of more than two signals. The iterativeoptimization is computationally expensive and the time taken to carryout this procedure renders it impractical in most situations.

SUMMARY

According to a first aspect of the invention, therefore, there isprovided a method for resolving individual signals in detector outputdata, comprising determining a signal form of signals present in thedata (or the impulse response), making parameter estimates of one ormore parameters of the signals, wherein the one or more parameterscomprise at least signal temporal position, and determining the energyof the signals from at least the signal form and the parameterestimates.

Thus, this method endeavors to characterize as much data as possible,but it will be appreciated that it may not be possible to adequatelycharacterize some data (which hence is termed ‘corrupt data’), as isdescribed below. It will be understood that the term ‘signal’ isinterchangeable in this context with ‘pulse’, as it refers to the outputcorresponding to individual detection events rather than the overalloutput signal comprising the sum of individual signals. It will also beappreciated that the temporal position (or timing) of a signal can bemeasured or expressed in various ways, such as according to the time (orposition in the time axis) of the maximum of the signal or the leadingedge of the signal. Typically this is described as the arrival time(‘time of arrival’) or detection time.

It will also be understood that the term ‘detector data’ refers to datathat has originated from a detector, whether processed subsequently byassociated or other electronics within or outside the detector.

The method may include constructing a model of the data from theparameter estimates, and determining the accuracy of the parameterestimates based on a comparison between the detector output data and themodel.

The signal form (or impulse response) may be determined by a calibrationprocess that involves measuring the detector's time domain response toone or more single event detections to derive from that data the signalform or impulse response. A functional form of this signal form may thenbe obtained by interpolating the data with (or fitting to the data) asuitable function such as a polynomial, exponential or spline. A filter(such as an inverse filter) may then be constructed from this detectorsignal form. An initial estimate of signal parameters may be made byconvolution of the output data from the detector with the filter. Signalparameters of particular interest include the number of signals and thetemporal position (or time of arrival) of each of the signals.

The particular signal parameters of interest can then be furtherrefined. Firstly, the estimate of the number and arrival times ofsignals is refined with the application of peak detection and athreshold. Secondly, knowledge of the number of signals and theirarrival time, coupled with the detector impulse response (and hencesignal form) makes it possible to solve for the energy parameters of thesignals.

The accuracy of the parameter estimation can be determined or‘validated’ by comparing a model (in effect, an estimate) of thedetector data stream (constructed from the signal parameters andknowledge of the detector impulse response) and the actual detectoroutput. Should this validation process determine that some parametersare insufficiently accurate, these parameters are discarded. Inspectroscopic analysis using this method, the energy parameters deemedsufficiently accurate may be represented as a histogram.

The method may include making the estimates of signal parameters inaccordance with the signal form (i.e. the impulse response of thedetector used for generating the signal). The method may includedetermining the signal form by a calibration process including measuringthe response of the detector to one or more single detections to derivea data based model of the signal form. In particular, the method mayinclude obtaining a functional form of the model by interpolating thedata with a function to generate the expected signal form. The functionmay be a polynomial, exponential or spline function.

The method may include designing a filter on the basis of thepredetermined form of the individual signals produced by the radiationdetector. The filter may be, for example, of matched filter or inversefilter form.

In one embodiment, the method includes using convolution of the detectoroutput and filter to make an initial estimate of the signal parameters.The method may include refining the estimate of the signal parameters.The method may include refining the estimate of signal number with apeak detection process. The method may include making or refining theestimate of signal temporal position by application of a peak detectionprocess. The method may include refining the estimate of signal energyby solving a system of linear equations, by matrix inversion or byiterative techniques.

In an embodiment of the invention, the method includes creating a modelof the detector output using the signal parameters in combination withthe detector impulse response. The method may include performing errordetection by, for example, comparing the actual detector output datawith the model of the detector output, such as by using least-squares orsome other measure of the difference between the data and the model.

The method may include discarding parameters deemed not sufficientlyaccurately estimated.

In one embodiment, the method includes presenting all sufficientlyaccurate energy parameters in a histogram.

The data may include signals of different forms. In this case, themethod may include determining where possible the signal form of each ofthe signals.

For example, in some detectors the signal form depends on the depthwithin the detector at which the radiation/detector interaction occurs.In other detectors, the signal form may depend on how much time haselapsed since the previous radiation/detector interaction occurred inthe same region of the detector.

In one embodiment, the method includes progressively subtracting fromthe data those signals that acceptably conform to successive signalforms of a plurality of signal forms, and rejecting those signals thatdo not acceptably conform to any of the plurality of signal forms.

In another aspect, the invention provides an apparatus for pulse pile-uprecovery from data comprising a plurality of signals output from aradiation detector. The term ‘recovery’ is used because data that wouldotherwise be unusable owing to pile-up is ‘recovered’ and rendereduseable. The apparatus of this aspect comprises a processor forreceiving the data in digitized form, and is programmed to determine thesignal form of each of said signals present in the data, to makeparameter estimates of one or more parameters of the signals, and todetermine the energy of the signals from at least the signal form andthe parameter estimates, wherein the one or more parameters comprise atleast signal temporal position.

The apparatus may include an analog to digital converter adapted toreceive the data, to convert the data into digitized form, and forwardthe data in digitized form to the processor. This would be of particularuse where the detector outputs analog data.

The processor may comprise a field programmable gate array (or an arraythereof). Alternatively, the processor may comprise a digital signalprocessor (or an array thereof). In a further alternative, the processorcomprises a field programmable gate array (or an array thereof) and adigital signal processor (or an array thereof). The apparatus mayinclude an analog front end that includes the analog to digitalconverter.

The apparatus may include an electronic computing device in datacommunication with the processor, for controlling the processor and fordisplaying an output of the processor. The apparatus may include theradiation detector.

The apparatus may be, for example, a metal detector, a landminedetector, a medical imaging apparatus, a mineral detection apparatus, anoil well logging apparatus, an unexploded ordnance detector, a cargoscreening apparatus, an X-ray fluorescence apparatus or an X-raydiffraction apparatus.

According to still another aspect of the invention, there is provided amethod for resolving individual signals in detector output data,comprising determining the form of signals present in the data, andmaking parameter estimates of one or more parameters of the signals fromat least the form, wherein the one or more parameters comprise at leastsignal temporal position.

According to another aspect of the invention, there is provided a methodfor pulse pile-up recovery from detector output data, comprisingdetermining the form of signals present in the data, making parameterestimates of one or more parameters of the signals, wherein the one ormore parameters comprise at least signal temporal position, anddetermining the energy of the signals from at least the form and theparameter estimates.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the invention may be more clearly ascertained, preferredembodiments will now be described, by way of example only, withreference to the accompanying drawing, in which:

FIG. 1 is a view of a gamma-ray spectroscopy apparatus according to anembodiment of the present invention;

FIG. 2 is a view of a Sodium Iodide NaI(Tl) gamma-ray detector of theapparatus of FIG. 1;

FIGS. 3 a, 3 b and 3 c are graphs illustrating pulse pile-up.;

FIG. 4 is a diagram illustrating the mathematical modeling of radiationdetection used by the signal processing method embodied in the apparatusof FIG. 1;

FIG. 5 is a diagram detailing the mathematical model of radiationdetection used by the signal processing method embodied in the apparatusof FIG. 1;

FIG. 6 is a schematic diagram of the apparatus of FIG. 1;

FIGS. 7 a, 7 b and 7 c are plots of unprocessed digitized data collecteddirectly from the output of the detector of FIG. 2 over time ranges of1000 microseconds, 100 microseconds and 10 microseconds respectively;

FIG. 8 is a schematic representation of the signal processing method forpulse pile-up recovery employed by the apparatus of FIG. 1 for analyzingspectroscopic data according to this embodiment of the invention;

FIG. 9 is a schematic flowchart of the signal processing method forpulse pile-up recovery employed by the apparatus of FIG. 1 for analyzingspectroscopic data according to this embodiment of the invention;

FIGS. 10 a, 10 b and 10 c are plots of the results at different stagesof the signal processing method of FIG. 9;

FIG. 11 are plots of gamma-ray spectra for a 137Cs source at variousinput count rates, processed with the method of FIG. 9;

FIG. 12 is a plot of the results of a computer simulation of the signalprocessing method of FIG. 9 prepared using a simulated data set producedby a digital nuclear pulse generator;

FIG. 13 is plot of the performance of the simulation of FIG. 12 for agamma-ray source over a range of count rates;

FIGS. 14 a, 14 b, 14 c and 14 d depict the results of applying thesignal processing method of FIG. 9 to the output of a 76 mm×76 mmNaI(Tl) gamma-ray detector;

FIGS. 15 a, 15 b, 15 c and 15 d depict the results of applying thesignal processing method of FIG. 9 to data collected with a HPGedetector; and

FIGS. 16 a, 16 b, 16 c and 16 d depict the results of applying thesignal processing method of FIG. 9 to the output of a Xenon gasproportional detector.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 is a schematic view of a gamma-ray spectroscopy apparatus adaptedto perform pulse pile-up recovery according to an embodiment of thepresent invention, with an item to be analyzed. The apparatus of FIG. 1includes a neutron generator (10) for generating neutrons forinteracting with an item under analysis or specimen (12), and a detectorunit (14), in the form of a scintillation based gamma-ray radiationdetector, for detecting gamma-ray radiation resulting from theinteraction of neutrons and the specimen (12). The detector unitincludes sensors or detector elements (16) that each has a scintillationcrystal (in this example, sodium iodide) coupled to a photomultipliertube (not shown). It will be appreciated that the apparatus couldreadily be modified, particularly by substituting a different form ofdetector unit, to detect other forms of radiation.

The apparatus also includes a signal processing unit (18) that comprisestwo parts: 1) an analog to digital converter which produces a digitaloutput corresponding to the analog output of the detector unit, and 2) aprocessing unit which implements digital signal processing (DSP)routines in accordance with the invention. The electrical output signalsof the photomultiplier tubes are connected to the signal processingunit. The apparatus also includes cables (20) and a computer (22) fordisplay, the former for coupling the output from the signal processingunit to the computer (22).

FIG. 2 is a view of one of the detector elements (16). The illustrateddetector element is in the form of a NaI(Tl) scintillation basedgamma-ray detector, and comprises a cylindrical housing in the form ofaluminium body (24) with a NaI(Tl) crystal (26) located therein at one(forward) end positioned between an aluminium outer end cap (28)(forward of the NaI(Tl) crystal (26)) and an inner optical window (30)(rearward of the NaI(Tl) crystal (26)). The detector includes aphotomultiplier tube (32) rearward of the optical window (30). Opticalcoupling fluid (34) may be used between the NaI(Tl) crystal (26) and theoptical window (30), and between the optical window (30) and thephotomultiplier tube (32).

When a gamma-ray interacts with the detector by passing into thedetector through the end cap (28), energy is transferred from thegamma-ray to electrons within the NaI(Tl) crystal (26). Upon theemission of ultra-violet photons the electrons lose said energy)promoting electrons within the crystal to excited states. Upon theemission of ultra-violet photons the electrons decay to lower energystates. The aforementioned ultra-violet photons pass through the opticalwindow to the photocathode (36) of the photomultiplier tube (32) wherethey are converted into photoelectrons and subsequently multiplied by anelectron multiplier (38) before arriving at the anode (40) of thephotomultiplier tube (32). A further multiplication stage can beprovided by a preamplifier (42). In this manner an electrical signal,whose amplitude is proportional to the energy of the incidentgamma-rays, is present at the detector output terminals (44) of thedetector. It will also be appreciated that the detector may additionallyinclude a mu metal magnetic shield (46) located about the sides (48) ofthe photomultiplier tube (32) and extending forwardly of thephotomultiplier tube (32) sufficiently far to surround a portion of theNaI(Tl) crystal (26).

Scintillation detectors of the kind last described have highefficiencies, that is, exhibit a high probability of detecting anincident gamma-ray. However, they also exhibit a relatively longdetector response time. The detector response time is the time requiredby the detector to detect an incident gamma-ray and return to a statewhere the next incident gamma-ray can be accurately detected. Radiationdetectors with long detector response times are thus prone to pulsepile-up. That is, the output, which ideally consists of completelydiscrete pulses each corresponding to the incidence of a singlegamma-ray, instead exhibits a waveform in which individual pulses canoverlap making them difficult to characterize.

FIGS. 3 a, 3 b and 3 c illustrate the effect of pulse pile-up, and showillustrative signals or pulses plotted as energy E versus time t (bothin arbitrary units). FIG. 3 a illustrates so-called ‘tail-end pile-up’where, depending on the type of pulse conditioning employed, the tail(50) of one pulse (51) can provide a significant positive or negativebias (positive in the illustrated example) to the amplitude of asubsequent pulse (52). Although the time displacement between the twopulses, Δt, is relatively large (when compared with the overall timeinterval for which the pulses prevail), the signal envelope or resultantwaveform (54) is significantly above zero at the arrival of the secondpulse (52).

The absence of a true zero signal state between the two pulses corruptsthe pulse characterization, as the amplitude of the second pulse isfalsely inflated by the tail of the first. FIG. 3 b illustrates anotherform of pulse pile-up, ‘peak pile-up’. Here two pulses (56) and (58)arrive closely spaced in time (i.e. the time displacement Δt between thepulses is small compared with the overall time interval over which thepulses prevail). The resultant output waveform (60) appears more or lessas a single pulse of somewhat greater amplitude than either of thecomponent pulses. In situations where the flux of gamma-rays through thedetector is extreme, it is not uncommon to have multiple events arrivingwithin the response time of the detector leading to multiple pile-upevents. Such a case is illustrated by FIG. 3 c. Multiple signals orpulses (such as those shown at 62) arrive with random time separation Δtand sum to produce a resultant waveform (64) from which the parametersof the component signals are difficult to extract.

One component of the method of addressing pulse pile-up according tothis embodiment is the estimation of certain parameters of the signalsor pulses; these parameters are the number, time-of-arrival and energyof all gamma-rays in the detector data stream. These parameters areestimated, according to this embodiment, by modeling the signals in thedata stream mathematically. The model employed in this embodimentincludes certain assumptions about the data and the apparatus, as arediscussed below.

FIG. 4 is a diagram that illustrates the modeling of the radiationdetection process. The radiation g(t) (70) is incident on the detector(72) represented by the measurement process m(t), resulting in outputdata from the detector y(t) (74). The addition of a sampling process(76) produces the digital detector data or ‘time-series’ x[n] (78).

It is possible to add to the above-described model some knowledge aboutthe physical processes of radiation detection. FIG. 5 illustrates a moredetailed mathematical model of the detection process shown in FIG. 4.The input g(t) to the detector is characterized by Equation 1, in whichthe input g(t) is assumed to be an unknown number (N) ofdelta-function-like impulses of random amplitude (α) and time of arrival(i). An illustrative example of such input is shown at (80).

$\begin{matrix}{{{g(t)} = {{\sum\limits_{i = 1}^{N}\; {\alpha_{i}{\delta \left( {t - \tau_{i}} \right)}\mspace{14mu} i}} = 1}},2,3,\ldots \mspace{11mu},{N.}} & (1)\end{matrix}$

The radiation detector is assumed to have a specific response to theincoming radiation, referred to as the detector impulse response d(t)(or, equivalently, the signal form of the signals in the data), which isillustrated at (82). The digitized version of the detector impulseresponse (i.e. signal form) is denoted d[n].

The output from the detector is shown at (86) and characterized byEquation 2, in which the detector output y(t) is the sum of an unknownnumber of signals of predetermined signal form d(t), with unknown energy(α) and unknown time of arrival (τ). Sources of random noise ω(t) (84)are also considered. The digital detector data x[n] (88) is produced bythe analog to digital converter (76).

$\begin{matrix}{{{y(t)} = {{{\sum\limits_{i = 1}^{N}{\alpha_{i}{d\left( {t - \tau_{i}} \right)}}} + {{\omega (t)}\mspace{14mu} i}} = 1}},2,3,\ldots \mspace{11mu},{N.}} & (2)\end{matrix}$

The digitized signal x[n] (which constitutes a time series of data) atthe output of the analog to digital converter (76), as illustrated at(88), is therefore given by

$\begin{matrix}{{{x\lbrack n\rbrack} = {{\sum\limits_{i = 1}^{N}{\alpha_{i}{d\left\lbrack {n - \Delta_{i}} \right\rbrack}}} + {\omega \lbrack n\rbrack}}},} & (3)\end{matrix}$

where d[n] is the discrete time form of the signal form d(t), Δ_(i) isthe delay in samples to the ith signal, and ω[n] is the discrete timeform of the noise. The digitized signal x[n] may also be written inmatrix form as

x=Aα+ω,  (4)

where A is an M×N matrix, the entries of which are given by

$\begin{matrix}{{A\left( {n,i} \right)} = \left\{ \begin{matrix}{d\left\lbrack {n - \Delta_{i}} \right\rbrack} & {\Delta_{i} \leq n < {\min \left( {M,{\Delta_{i} + T - 1}} \right)}} \\0 & {{otherwise}.}\end{matrix} \right.} & (5)\end{matrix}$

Also, T is the length of d[n] in samples, M is the total number ofsamples in the digitized signal x[n], α is the vector of N signalenergies, and ω is the noise vector of length M. Matrix A may also bedepicted as follows:

$\quad{A = {\begin{bmatrix}0 & 0 & \cdots & 0 \\\vdots & \; & \; & \; \\0 & \vdots & \; & \; \\{d\lbrack 1\rbrack} & \; & \; & \vdots \\{d\lbrack 2\rbrack} & 0 & \; & \; \\\vdots & {d\lbrack 1\rbrack} & \; & \; \\{d\lbrack T\rbrack} & \; & \; & \; \\0 & \vdots & \ddots & \; \\\; & \; & \; & {d\lbrack 1\rbrack} \\\vdots & {d\lbrack T\rbrack} & \; & {d\lbrack 2\rbrack} \\\; & \; & \; & \vdots \\0 & \cdots & 0 & {d\left\lbrack {r < T} \right\rbrack}\end{bmatrix}\begin{matrix}\left. \leftarrow{{row}\mspace{14mu} \Delta_{1}} \right. \\\left. \leftarrow{{row}\mspace{14mu} \Delta_{2}} \right. \\\left. \leftarrow{{row}\mspace{14mu} \Delta_{N}} \right.\end{matrix}}}$

Thus, the columns of matrix A contain multiple versions of the signalform. For each of the individual columns the starting point of thesignal form is defined by the signal temporal position. For example, ifthe signals in the data arrive at positions 2, 40, 78 and 125, column 1of matrix A will have ‘0’ in the first row, the 1st datum point of thesignal form in the second row, the 2nd datum point of the signal form inthe 3rd row, etc. The second column will have ‘0’ up to row 39 followedby the signal form. The third column will have ‘0’ up to row 77; thefourth column will have ‘0’ up to row 124 and then the signal form.Hence the size of matrix A is determined by the number of identifiedsignals (which becomes the number of columns), while the number of rowsdepends on the number of samples in the time series.

The signal processing method of this embodiment thus endeavors toprovide an accurate estimate of some unknown parameters of the detectordata, including not only the number of component signals (N) in thedetector output but also the energy (α) and time-of-arrival (τ) of eachof the component signals.

Signal Processing Method

FIG. 6 is a schematic diagram of the functional elements of thegamma-ray spectroscopy apparatus of FIG. 1, and is provided to explainin more detail the signal processing method for pulse pile-up recoveryemployed by the apparatus of FIG. 1. Referring to FIG. 6, the radiationdetector unit (14) is connected to a pulse processing board (92) via ananalog front end (AFE 94). The purpose of the AFE (94) is to digitizethe signal produced by the radiation detector unit (14) by performinganalog to digital conversion at, in this embodiment, 125 MHz with 12-bitconversion accuracy.

FIGS. 7 a, 7 b and 7 c illustrate the waveform resulting from suchdigitization, over time ranges of 1000 microseconds, 100 microsecondsand 10 microseconds respectively. The various peaks in these figurescorrespond to the detection of respective gamma-rays. Some peaks appearas discreet signals or pulses (110, 112) which may indicate the presenceof only a single gamma-ray. Other peaks are due to the pile-up either oftwo peaks (116) or of three or more peaks (114).

After the output of the radiation detector unit (14) has been digitizedby the AFE (94), the signal processing method for pulse pile-up recoveryis implemented. Referring again to FIG. 6, the digital signal producedby the AFE (94) is passed into the pulse processing Field ProgrammableGate Array (FPGA) (96). The pulse processing FPGA (96) then implementsthe pulse processing method of this embodiment; a digital signalprocessing coprocessor (98) may optionally be used to assist the pulseprocessing FPGA (96) to implement the pulse processing method. Variablesrequired by the pulse processing FPGA (96) and data produced at interimsteps of the pulse processing method are optionally stored in memory(100). The signal processing is controlled via a Data/Control Interface(102) which, in conjunction with a Control Processor (104), can be usedto modify the implementation of the signal processing. The output datafrom the signal processing method can be displayed on a display (106)via the Data/Control Interface (102). Display (106) is provided in acomputer that may, if desired, be used to perform post-processing andsystem control.

FIG. 8 is a schematic diagram of the signal processing method for pulsepile-up recovery of radiation signals in the detector time series ofthis embodiment. The digitized detector signal (from AFE (94)) forms theinput (120) for this signal processing method. Offline SystemCharacterization (122) is used to determine the detector impulseresponse unique to the particular digitized detector signal.Characterization data generated in System Characterization phase (122)is use in a Pulse Localization phase (124). The Pulse Localization phase(124) estimates, in real-time, the number and temporal position (ortime-of-arrival) of radiation pulses within the digitized detectorsignal. In a Pulse Identification phase (126), the digitized detectorsignal, the detector impulse response and the output from the PulseLocalization phase (124) are used to determine the energy of the signalsor pulses. Validation (128) involves comparing the output of the PulseIdentification phase (126) with the digitized detector signal (120). Ifthis comparison indicates that any of the pulse parameters have beenestimated inaccurately, those parameters are rejected so that only validdata is output (130). The error signal generated in the Validation phase(128) is also employed in System Characterization (122). Incircumstances where the detector impulse response may change over time,such as owing to the aging of components, temperature variations orincreased radiation fluxes, System Characterization (122) updates thedetector impulse response online and adaptively by employing the errorsignal. Such updating of the detector impulse response may be performedwith any suitable adaptive method, such as least mean squaresadaptation, normalized least mean squares adaptation or recursive leastsquares adaptation as described, for example, by S. Haykin [AdaptiveFilter Theory, 4th Ed, Prentice Hall, 2002].

FIG. 9 is a flow diagram of the signal processing method of thisembodiment. At step (140), calibration is performed. This involves DataRegularization or Conditioning (142), Data Selection and Fitting (144)and Optimal Filter Construction (146). In Data Regularization (142),calibration data (signals recorded at a low incident radiation flux) areloaded from data files, the integrity of these calibration data ischecked and any bias in the baseline of the data removed. Data Selectionand Fitting (144) involves selecting only that data corresponding to thedetection of single radiation events and constructing a data based modelof the detector impulse response. A functional form of this model isthen obtained by fitting a suitable function to the data, such as apolynomial, exponential or spline function. This results in the expectedimpulse response of the detector d[n]. Optimal Filter Construction (146)employs this detector impulse response to construct a suitable filterfor the detector, such as an inverse filter or a matched filter.

At step (150) data is acquired, but may be affected by significant pulsepile-up. The data may be input (152) either from a file or directly fromthe detector elements (16).

At step (160) signal processing routines are applied to determine theamplitude and timing parameters of the signals in the time series.Firstly the data is conditioned (162) to remove any bias in the baselineof the data. Next, the detector data is convoluted (164) with the filterderived in step (146) to provide an initial estimate of thetime-of-arrival parameters (τ) and number of pulses (N). The timingparameters and estimate of the number of pulses are then further refined(166) using a suitable peak detection process, and the energy parameter(α) is determined from τ, N and the detector impulse response d[n] (suchas by linear programming, matrix inversion or convolution techniques).Finally, from the number (N), energy (α), timing (Δi) and detectorimpulse response (d[n]), an estimate of the detector data stream({circumflex over (x)}[n]) is made (168).

The parameter vector (α) may be determined by linear programming or bysolving the system of linear equations defined in Equation 4 using asuitable method for solving such systems of equations, such as one ofthose described, for example, by G. H. Golub and C. F. Van Loan [MatrixComputations, 2nd Ed, Johns Hopkins University Press, 1989].

At step (170) the validation phase (128) referred to above is performed,which may be referred to as error checking as, in this embodiment,validation involves determining an error signal e[n], computedsuccessively for the set of samples corresponding to each signal i where1≦i≦N (N being the total number of signals in the data stream). Thiserror signal is calculated by determining (172) the squares of thedifferences between the time series data x[n] and the model baseddata-stream ({circumflex over (x)}[n] from step (168)); e[n] is thus thesquare of the difference between x[n] and {circumflex over (x)}[n], asgiven in Equation 6.

e[n]=(x[n]−{circumflex over (x)}[n])²  (6)

If e[n] exceeds a predetermined threshold, these parameters are rejected(174) as this condition indicates that the signal parameters do notproduce a model of the respective signal that acceptably conforms tothat signal (that is, is sufficiently accurate); the relevant signal isdeemed to constitute corrupted data and excluded from furtherspectroscopic analysis. The threshold may be varied according to thedata and how closely it is desired that the data be modeled; generally,therefore, in any particular specific application, the method ofvalidation and definition of the threshold are chosen to reflect therequirements of that application.

One example of such a threshold is the signal energy αi multiplied by asuitable factor, such as 0.05. Validation will, in this example, deemthat the model acceptably conforms to the data constituting signal iwhen:

e[n]>0.05α_(i)  (7)

Validation may be performed by defining the error signal and thresholdin any other suitable way. For example, the error signal may be set tothe absolute value of the error. The threshold may be defined to be amultiple other than 0.05 of the signal amplitude. Another thresholdcomprises a number of noise standard deviations.

Decreasing the threshold (such as by decreasing the coefficient of αi inEquation 7) enables improved energy resolution at lower throughput,while increasing the threshold enables improved throughput at reducedenergy resolution.

At step (180) a decision is made as to whether there is sufficient data.If not, processing continues at step (150). Otherwise, the methodproceeds to step (190). At step (190) a gamma-ray energy spectrum iscreated. The gamma-ray energy parameters determined at step (166), whichwere deemed to be of sufficient accuracy at step (174), are represented(192) in the form of a histogram. This is the gamma-ray energy spectrumon which spectroscopic analysis may be performed.

Results of Signal Processing Method

FIGS. 10 a, 10 b and 10 c are plots of the results at various stages ofprocessing of the digital signal processing method described above byreference to FIGS. 8 and 9, for digitized data collected with ascintillation gamma-ray detector. The detector data stream was digitizedby an analog to digital converter at 125 MHz and 12 bit accuracy; thegamma-ray source used was a 137Cs source with a primary gamma-rayemission of 661.7 keV.

Scintillation detectors employ light generated by the detector/radiationinteraction to detect and measure that incident radiation. Ascintillation detector may comprise organic scintillators or inorganicscintillators. Organic scintillators include both organic crystallinescintillators and liquid organic solutions (where the scintillatingmaterial has been dissolved to form a liquid scintillator, which canthen be plasticized to form a plastic scintillator. Inorganicscintillators include crystalline scintillators such as NaI(Tl), BGO,CsI(Tl) and many others, and photo switch detectors (in which acombination of two or more dissimilar scintillators are opticallycoupled to a common PMT to exploit the differing decay times of thescintillators to determine where a radiation/detection interaction hasoccurred).

In this example the detector comprised a 76 mm×76 mm NaI(Tl) gamma-rayscintillation detector. FIG. 10 a is a plot of a portion of thedigitized detector data (200) prior to processing by the signalprocessing method plotted as energy E(keV) versus time t(μs), togetherwith the results (for example, at 210) of the signal processing methodplotted in terms of the temporal position and energy of the componentsignals. For example, what may appear to be a single peak (220) in theoriginal digitized detector data (200) at approximately 75.8 μs has beenresolved into two distinct signals (222, 224) at respectively 75.3 and75.7 μs.

From the determined temporal positions, energies and forms of thesignals it is possible to generate a model of the detector data. FIG. 10b is a plot of the resulting data model (230), shown as energy E(keV)versus time t(μs), of that portion of the digitized detector data stream(200) shown in FIG. 10 a. An inverted error plot (240), comprising aplot of the squares of the differences between the detector data (200)and the data model (230), is also shown, and indicates the error in themodel (230). The error signal is small where the model (230) has trackedthe output of the detector accurately, but the error becomes large whenthere are inconsistencies between the model (230) of the detector dataand the detector data (200) itself. Based on this error signal (240), adecision can be made as to whether to accept or reject the signalparameters estimated by the signal processing method.

FIG. 10 c is a gamma-ray energy spectrum (250), shown as a log-linearplot, produced by the signal processing method. The energy parametersthat have been accepted are plotted as a histogram, where the horizontalaxis represents the energy E(keV) of each signal in a respective bin,and the vertical axis represents the number of counts N of that energydetermined to have been detected in the collection period (in thisexample, 1 s).

FIG. 11 is a plot of exemplary gamma-ray energy spectra, collected usinga sodium iodide NaI(Tl) gamma-ray detector. The gamma-ray energy spectrashown in FIG. 11 demonstrate the performance of the signal processingmethod for pulse pile-up recovery at a range of count rates. Theexperimental data were collected using a 76 mm×76 mm Canberra brandNaI(Tl) gamma-ray detector (model number 802) coupled to a detector base(model number 2007); no preamplifier was used. The signal processinghardware was connected to the dynode output of the detector base via a65 MHz 14-bit analog to digital converter.

The NaI(Tl) crystal was irradiated with a collimated gamma-ray beam,which ensured that the central portion of the detector was illuminatedwith an essentially parallel beam of gamma-rays; the beam diameter was50 mm.

Two 137Cs gamma-ray sources of 0.37 GBq and 3.7 GBq, in combination withthree calibrated aluminium transmission filters, were used to obtain arange of gamma-ray fluxes at the detector face. The detector to sourcedistance remained constant during data collection.

Referring to FIG. 11, the spectra (260), (262), (264), (266), (268) and(270) were collected at count rates of respectively 529 kHz, 230 kHz,167 kHz, 124 kHz, 67 kHz and 9 kHz. As would be expected, the energyresolution of the data collected with the apparatus and processed withthe method of this embodiment deteriorated as the count rate increased.Expressed as a percentage of the peak energy (i.e. 661.7 keV), the fullwidth at half maximum (FWHM) of the peak was found to be, respectively,9.6% 7.3%, 7.1%, 6.9%, 6.7% and 6.7%. For count rates of 9 kHz to 230kHz, the energy resolution of the 137Cs gamma-ray energy peak at 661.7keV remained less than 7.5%; that is, despite more than a 25 foldincrease in the count rate from the NaI(Tl) detector, the energyresolution at 661.7 keV decreased by less than 0.5%.

The performance of the signal processing method of this embodiment isalso illustrated in FIG. 12 and FIG. 13. These two figures weregenerated from the results of a computer simulation, in which the inputcount rate could be accurately controlled hence enabling a very widerange of input count rates to be considered. FIG. 12 is a log-log plotof the throughput of the signal processing method (i.e. that portion ofthe input count rate accurately detected) against input count rate from0.1-2.5 MHz. The theoretical limit (i.e. where the throughput equals theinput) is shown with a dashed line. This figure demonstrates that, overa very wide range of input count rates, the throughput of the signalprocessing method remains greater than or equal to 90%.

FIG. 13 is a linear-log plot comparable to FIG. 12 but with percentagethroughput plotted against input count rate from 0.005-10 MHz. Inaddition, FIG. 13 includes plots of the energy resolution and peakposition performance of the signal processing method of this embodiment.The energy resolution of the 137Cs peak degrades by less than 10% over0-2.5 MHZ, and the peak position shows very little change over thatrange.

FIGS. 14 a, 14 b, 14 c and 14 d also depict the results of applying thesignal processing method for pulse pile-up recovery of this embodimentto the output of a 76 mm×76 mm NaI(Tl) gamma-ray detector. Approximately14 μs of data was used to generate the data plotted in these figures.The figures are plots of energy E in arbitrary units against time t(μs).

FIG. 14 a is a plot of the output of the AFE (94): an analog to digitalconversion rate of 65 MHz and 14 bit resolution was used to covert thetime varying voltage output of the detector to digital data. FIG. 14 bis a plot of the results of applying the method. The temporal positionsof the signals (depicted as vertical lines) have been resolved, as havethe energies of the component signal (depicted as crosses). The temporalposition and the energy of the component signal were used as describedabove, in conjunction with the signal form, to determine a model of thegamma-ray detector output: the resulting model is plotted in FIG. 14 c.

The digitized output of the gamma-ray detector was compared with themodel of the gamma-ray detector output to derive an estimate of theerror made in characterizing the gamma-ray detector output. This errorsignal is plotted in FIG. 14 d. It is then possible, on the basis ofthis error signal, to determine thresholds for the exclusion of signalparameter estimates, such as the decision to accept or reject anestimate of signal energy may be determined by the magnitude or theerror near the position of a signal peak.

FIGS. 15 a, 15 b, 15 c and 15 d depict the results of applying thesignal processing method for pulse pile-up recovery of this embodimentto data collected with a semiconductor (or solid state) detector. Suchdetectors employ the interaction of incident radiation with theelectrons in the crystalline lattice of the semiconductor, formingelectron hole pairs. Examples of these detectors include High-PurityGermanium (HPGe) detectors, Silicon Diode detectors, semiconductor driftdetectors (such as Silicon Drift detectors), Cadmium Telluride (CdTe)detectors and CZT detectors.

Hence, the apparatus of FIG. 1 was employed, though with a detector unitin the form of a Canberra Industries brand High Purity Germanium (HPGe)detector substituted for detector unit (14), and with a 57Co gamma-raysource (whose two principal gamma-rays have energies of 122.1 and 136.5keV) rather than a neutron source and specimen. The output of the HPGedetector was fed through a pre-amplifier and then into an Ortec brandpulse shaping amplifier. Approximately 92 μs of data was collected, fromwhich was generated the data plotted in FIGS. 15 a, 15 b, 15 c and 15 das energy E in arbitrary units against time t(μs). FIG. 15 a is a plotof the output of the AFE (94). The time varying voltage output of thedetector was converted to digital data at an analog to digitalconversion rate of 65 MHz with 14 bit resolution. FIG. 15 b is a plot ofthe results of applying the method. The temporal positions of thesignals (depicted as vertical lines) have been resolved, as have theenergies of the component signal (depicted as crosses). The temporalposition, the energy of the component signal and the signal form wereused to determine a model of the processed HPGe detector output, whichis plotted in FIG. 15 c.

FIG. 15 d is a plot of the error signal, derived from a comparison ofthe digitized processed output of the HPGe detector and the model ofthat output. This error signal can again be used to determine thresholdsfor the exclusion of signal parameter estimates.

FIGS. 16 a, 16 b, 16 c and 16 d depict the results of applying thesignal processing method for pulse pileup recovery of this embodiment tothe output of a gas proportional detector used for detecting X-rays. Gasproportional detectors are a class of detector whose behavior is similarto that of solid state detectors. Gas proportional detectors rely on theinteraction of the radiation with a gas in a chamber. An electric fieldis created in the chamber between an axial wire and the walls of thechamber. Radiation passing through the gas ionizes the gas, whichproduces electrons that then collect on the wire owing to the electricfield, and are output as the detector data.

Thus, the apparatus of FIG. 1 was employed, though with a detector unitin the form of a Xenon gas proportional detector substituted for thedetector unit (14), and with an X-ray generator from an X-raydiffraction apparatus rather than a neutron source and specimen.Approximately 300 μs of data was used to generate the data plotted inFIGS. 16 a, 16 b, 16 c and 16 d, which plot energy E in arbitrary unitsagainst time t(μs). A significantly longer data collection period wasused compared with that of the previous examples, owing to therelatively long decay time of the xenon gas proportional detector (ofthe order of 50 μs or more). For this reason also the sampling rate ofthe AFE (94) was reduced.

FIG. 16 a is a plot of the output of the AFE (94); in this example ananalog to digital conversion rate of 15 MHz and 14 bit resolution wasused to covert the time varying voltage output of the detector todigital data. FIG. 16 b is a plot of the results of applying the method.The temporal positions of the X-ray signals (depicted as vertical lines)have been resolved, as have the energies of the component signal(depicted as crosses). The temporal position and the energy of thecomponent signal were used as described above, in conjunction with thesignal form, to determine a model of the Xenon gas proportional detectoroutput: the resulting model is plotted in FIG. 16 c.

The digitized output of the Xenon gas proportional detector was comparedwith the model of the Xenon gas proportional detector output to derivean estimate of the error made in characterizing the Xenon gasproportional detector output. This error signal is plotted in FIG. 16 d.This error signal can then be used to determine thresholds for theexclusion of signal parameter estimates, such as the decision to acceptor reject an estimate of signal energy may be determined by themagnitude or the error near the position of a signal peak.

Plural Signal Forms

For some detector types, such as large volume solid state detectors, theform of a given signal may be one of a plurality of possible signalforms. This may be intrinsic to the detector type, or be due totemperature or other measurement-specific factors.

For example, a CsI(Tl) detector is a scintillation detector that,depending on whether a neutron or gamma-ray is being detected, exhibitstwo distinct signal forms. Solid state radiation detectors can exhibit atime-varying signal form, even when detecting only one form ofradiation; large volume High Purity Germanium (HPGe) detectors, forexample, can produce an output signal whose form depends on the specificsite of interaction between the radiation and the detector. Theinteraction of radiation with the Germanium crystal of a HPGe detectorproduces a multitude of electron-hole pairs; radiation induced charge iscarried by both the electrons and the holes. However, the electrons andholes travel through the HPGe detector at different velocities, so thecharge pulse produced by the electrons generally has a different formfrom that produced by the holes. Thus, the pulse produced by thedetector (being the sum of the charges carried by both the electrons andholes) has a form dependent on the location of interaction.

Hence, the plurality of signal forms are the result of these variedphysical mechanisms. The respective signal forms may be denoted d1[n],d2[n], . . . , dQ[n], where Q is the total number of different signalforms that may be generated by a particular detector type. Each of thepossible signal forms is characterized in the same way that the signalform of data having a single signal form is characterized. With pluralsignal forms, however, the calibration process must be extended for anappropriate length of time to ensure that all of the possible signalforms have been identified and characterized; the estimation of signalparameters, including temporal position and signal energy, can beperformed once the form of each signal in the data stream has beenidentified. In order to estimate these signal parameters correctly, anumber of possible extensions of the method described above (for datawith a single signal form) may be employed.

1. The signal parameters, including signal temporal position and signalenergy, may be estimated for each signal in the data stream by treatingall signals in the data stream as having the same form, such as of thefirst signal, viz. d1[n]. The parameters for those signals that do notacceptably conform to signal form d1[n] are rejected at the validationphase; signals for which the parameters have been estimated successfullyand thus acceptably conform to signal form d1[n] are subtracted from thedata stream. This process is repeated successively for d2[n] up todQ[n], where at each stage signal parameters are estimated for signalsthat are of the signal form used at that stage. At each stage matrixEquation 4 is solved with matrix A constructed repeatedly using, initeration p, the signal form dp[n]. At the conclusion of the process,those signals that have not passed the validation phase for any of theplurality of signal forms are rejected as not acceptably conforming toany of the plurality of signal forms.

2. In a variation of the first approach, the signal parameters areestimated for each of the signal forms in turn, but the signal estimatesare not subtracted at each stage. Instead, the estimated signals areused in a final signal validation stage to determine the signal form andsignal parameters that provide the best overall estimate of the datastream. This allows for the possibility that a signal is incorrectlyestimated to be of one form, when it is actually of a form that has notyet been used to estimate the signal parameters.

3. In a further variation of the first approach, it may be possible tomodel each of the signal forms dp[n] as a linear combination of twosignal forms, termed d1[n] and d2[n] for convenience. Hence, the pthsignal form dp[n] is modeled as:

d _(p) [n]=(a.d ₁ [n]+b.d ₂ [n])  (8)

where a and b are unknown constants that can be determined directly fromthis equation if necessary. In order to solve the matrix equation inthis case, the matrix equation is extended to be:

$\begin{matrix}{{x = {{\left\lbrack {A_{1}\mspace{20mu} \vdots \mspace{20mu} A_{2}} \right\rbrack \begin{bmatrix}\gamma \\\cdots \\\beta\end{bmatrix}} + \omega}},} & (9)\end{matrix}$

where the sub-matrices A₁ and A₂ are formed from the signal forms d₁[n]and d₂[n] respectively using Equation 5. The vector of unknown signalenergies a has been redefined as being made up of vectors γ and β, sothat the energy of the actual signal form of signal i can be estimatedas α_(i)=γ_(i)+β_(i). The new system of linear equations is solved usingthe same methods as those used to solve the earlier matrix equation,Equation 4. It should be noted that this approach eliminates the needfor explicitly estimating the unknown constants α and b, and also allowsfor the possibility that the signal form may be from a continuum ofpossible signal forms that can be represented as a linear combination ofthe two signal forms d₁[n] and d₂[n].

Thus, this approach permits a practically unlimited number of signalforms to be represented.

4. In a further variation of approach 3, the procedure of decompositionof each of the plurality of signal forms into a linear combination ofjust two signal forms may be extended to the general case where theplurality of signal forms may be decomposed as a linear combination ofan arbitrary number of signal forms. The matrix A and the signal energyvector a is augmented accordingly.

Modifications within the scope of the invention may be readily effectedby those skilled in the art. It is to be understood, therefore, thatthis invention is not limited to the particular embodiments described byway of example hereinabove.

In the claims that follow and in the preceding description of theinvention, except where the context requires otherwise owing to expresslanguage or necessary implication, the word “comprise” or variationssuch as “comprises” or “comprising” is used in an inclusive sense, i.e.to specify the presence of the stated features but not to preclude thepresence or addition of further features in various embodiments of theinvention.

Further, any reference herein to prior art is not intended to imply thatsuch prior art forms or formed a part of the common general knowledge.

1. A method of resolving individual signals in a radiation detectoroutput data, the method comprising: obtaining a signal formcharacterizing the detector; obtaining digitized detector output data ina form of a digital time series; making parameter estimates of one ormore parameters of at least one signal present in the detector outputdata, wherein the one or more parameters comprise at least a signaltemporal position of the at least one signal; forming a mathematicalmodel based on the digital time series and as a function of at least thesignal form, the temporal position of the at least one signal, and anamplitude of the at least one signal; and determining the amplitude ofthe at least one signal based on said mathematical model, the amplitudebeing indicative of a radiation event.
 2. The method as recited in claim1, wherein obtaining the signal form comprises receiving data about thesignal form from a memory.
 3. The method as recited in claim 1, whereinobtaining the signal form comprises deriving the signal form based on atleast one signal present in the detector output data.
 4. The method asclaimed in claim 1, further comprising determining energy of the atleast one signal based on at least the signal form and the parameterestimates.
 5. The method as recited in claim 1, further comprisingdetermining accuracy of the parameter estimates based on a comparisonbetween the detector output data and the mathematical model.
 6. Themethod as recited in claim 1, wherein obtaining the signal formcomprises determining the signal form by measuring a response of thedetector to one or more detections.
 7. The method as recited in claim 6,further comprising interpolating the detector output data with afunction to generate an expected signal form, wherein the functioncomprises a polynomial, exponential or spline function.
 8. An apparatusfor resolving individual signals in a radiation detector output data,the apparatus comprising a processor configured to: obtain a signal formcharacterizing the detector; obtain digitized detector output data in aform of a digital time series; make parameter estimates of one or moreparameters of at least one signal present in the detector output data,wherein the one or more parameters comprise at least a signal temporalposition of the at least one signal; form a mathematical model based onthe digital time series and as a function of at least the signal form,the temporal position of the at least one signal, and an amplitude ofthe at least one signal; and determine the amplitude of the at least onesignal based on the mathematical model, the amplitude being indicativeof a radiation event.
 9. The apparatus as recited in claim 8, whereinthe processor is configured to obtain the signal form from a memory. 10.The apparatus as recited in claim 8, wherein the processor is configuredto obtain the signal form by deriving the signal form based on at leastone signal present in the detector output data.
 11. The apparatus asrecited in claim 8, wherein the processor is further configured todetermine energy of the at least one signal based on at least the signalform and the parameter estimates.
 12. The apparatus as recited in claim8, wherein the processor is further configured to determine accuracy ofthe parameter estimates based on a comparison between the detectoroutput data and the mathematical model.
 13. The apparatus as recited inclaim 8, wherein the processor is further configured to determine thesignal form by measuring a response of the detector to one or moredetections.
 14. The apparatus as recited in claim 13, wherein theprocessor is further configured to interpolate the detector output datawith a function to generate an expected signal form, wherein thefunction comprises a polynomial, exponential or spline function.
 15. Adata storage medium storing instructions, when executed by a processor,causing the processor to perform a method of resolving individualsignals in a radiation detector output data, the method comprising:obtaining a signal form characterizing the detector; obtaining digitizeddetector output data in a form of a digital time series; makingparameter estimates of one or more parameters of at least one signalpresent in the detector output data, wherein the one or more parameterscomprise at least a signal temporal position of the at least one signal;forming a mathematical model based on the digital time series and as afunction of at least the signal form, the temporal position of the atleast one signal, and an amplitude of the at least one signal; anddetermining the amplitude of the at least one signal based on saidmathematical model, the amplitude being indicative of a radiation event.16. The data storage medium as recited in claim 15, wherein obtainingthe signal form comprises receiving data about the signal form from amemory.
 17. The data storage medium as recited in claim 15, whereinobtaining the signal form comprises deriving the signal form based on atleast one signal present in the detector output data.
 18. The datastorage medium as recited in claim 15, further comprising instructionsthat cause the processor to determine energy of the at least one signalbased on at least the signal form and the parameter estimates.
 19. Thedata storage medium as recited in claim 15, further comprisinginstructions that cause the processor to determine accuracy of theparameter estimates based on a comparison between the detector outputdata and the mathematical model.
 20. The data storage medium as recitedin claim 15, further comprising instructions that cause the processor todetermine the signal form by measuring a response of the detector to oneor more detections.